All you need is N: Baryon spectroscopy in two large N limits

TL;DR

This paper compares two large N_c limits in baryon spectroscopy, analyzing their predictions for mass relations and symmetries, and discusses a hybrid limit's theoretical appeal versus phenomenological challenges.

Contribution

It provides a comparative analysis of fundamental and antisymmetric large N_c limits and introduces a hybrid approach, evaluating their predictions against experimental data.

Findings

Both large N_c limits predict similar mass relations consistent with experiments.

Emergent spin-flavor symmetry leads to vanishing mass combinations at specific orders.

The hybrid large N_c limit faces phenomenological difficulties despite its theoretical appeal.

Abstract

The generalization of QCD to many colors is not unique; each distinct choice corresponds to a distinct 1/N_c expansion. The familiar 't Hooft N_c -> \infty limit places quarks in the fundamental representation of SU(N_c), while an alternative approach places quarks in its two-index antisymmetric representation. At N_c=3 these two 1/N_c expansions coincide. We compare their predictions for certain observables in baryon spectroscopy, particularly mass combinations organized according to SU(3) flavor breaking. Each large N_c limit generates an emergent spin-flavor symmetry that leads to the vanishing of particular linear combinations of baryon masses at specific orders in the expansions. Experimental evidence shows that these relations hold at the expected orders regardless of which large N_c limit one uses, suggesting the validity of either limit in the study of baryons. We also consider a hybrid large N_c limit in which one flavor is taken to transform in the two-index antisymmetric representation and the rest of the flavors are in the fundamental representation. While this hybrid large N_c limit is theoretically attractive, we show that for a wide class of observables it faces some phenomenological difficulties.